2.71: Kinematics with trigonometric velocity

0606/23/O/N/17 — Question 7 · 8 marks

A particle moves in a straight line through a fixed point OO. The velocity of the particle, vv in ms1\text{ms}^{-1}, at time tt seconds after passing through OO is given by v=3cos2t1v = 3\cos 2t - 1 for t0t \ge 0.
(i)
Find the value of tt when the particle is first at rest.
[2]
(ii)
Find the displacement from OO of the particle when t=π4t = \dfrac{\pi}{4}.
[3]
(iii)
Find the acceleration of the particle when it is first at rest.
[3]